46. From the fame maxim is deduced a method of proving the truth of any operation in Addition, viz. by parting or feparating the given Numbers into two parcels (or more, according to the largeness of it), and then adding up each parcel by itself: For if those particular fums, fo found, be added into one fum, and that fum prove equal, or the fame with the total fum first found, then all is right; if not, care must be taken to discover and correct the error.

Note, This laft method may be usefully applied in the addition of long columns, in order to eafe the memory; and the fame may be proved by dividing them into different parcels.

47. Another method of proof is, to perform the operation again, beginning with the uppermoft figure of each rank, and adding downwards.

Note, 1. The fum of two or more even numbers will be an even number.

2. The fum of two odd numbers will be an even number. 3. The fum of two numbers; one even, the other odd, will be an odd number.

4. If more than two odd numbers be added together; the fum will be even, when the number of its parts, fo to be added together, is even; but odd, if the number of parts be odd.

5. If even numbers be intermixed with odd, the fum will be even or odd, according as the number of odd parts be even or odd.

Chap. III. 48. When numbers given to be added, exprefs things of diverfe denominations; firft write them down orderly (according to the Examples in Chap. II.) then after a line is drawn under them all, begin to add the numbers of the least denomination, and if the fum of them amounts to one integer, or many integers of the next greater denomination, with fome excefs of the less denomination, fet down that excefs, or a cypher when there is no excess, under the line, fo as it may ftand under the least denomination, and keep the said integer or integers in mind, to be added to thofe of the next greater denomination on the lefthand; but when the fum of the numbers of the least denomination does not amount to one integer of the next greater denomination, fet down the fum itself under the line: Then add the integer or integers kept in mind (when any happens) to the numbers of the next greater denomination on the left-hand, and proceed to add them, as alfo thofe of every greater denomination, in like manner as above is directed; until you come to the numbers of the greatest (or higheft) denomination, which are to be added according to Art. 43. and 44. So these several fums 241. 135. 5 d. 3f. alfo 12 l. os. 8 d. and 51. 18s. od. 2fbeing propos'd to be added, their total fum is 427. 12s. 2 d. If. For having written them down orderly according to Art. 21. and drawn a line underneath, begin with the farthings firft, and say, two farthings and three farthings make five farthings, that is one penny with a farthing over and above; wherefore fetting down I under the denomination of farthings, carry one penny to the denomination of pence; then fay, 1, 8, and 5 pence make 14 pence, which contain one thilling and two-pence; wherefore writing two under the denomination of pence, carry one fhilling to the denomination of fhillings; then adding the faid I fhilling to 18 fhillings and 13 fhillings, the fum will found 1 pound and 12 fhillings; wherefore setting down 12 under the denomination of fhillings, carry 1 pound in mind to the denomination of pounds, faying, I pound in mind, together with 5, 2, and 4 pounds, which ftand in the first rank of pounds, make 12 pounds; wherefore (according to Art. 44.) write 2, the excefs above 10, under the faid first rank of pounds, and carry 1 in mind for the faid 10 to the fecond rank of pounds; then saying, in like manner, I in mind, together with 1 and 2, which ftand in the second rank of pounds make 4, which write under the line; that done, the total of the three given fums appears to be 427. 12 s. and 2 d. 1 f.

7. S. d. f.

24

12

05

42

13.05.3

00 08 O

18. 00 2

12

02. I

In like manner 3lb. 050z. 19p.w. 15 gr.
Alfo olb. 10 oz. 6 p.w. ogr.

Alfo 2 lb. ooz. 3p.w. 7 gr. And o lb. 90%. op.w. 17 gr. being given to be added together, their fum will be found 7 lb. 010%. 9p.w. 15gr. and the work will stand

thus:

Note, In adding together the numbers in the laft example, it must be remember'd, that twenty-four grains make one pennyweight; twenty penny-weights one ounce; and twelve ounces one pound Troy (as before is declared in Art. 22.); and then you are to proceed according to Art. 48.

More Examples are thefe following, which prefuppose the learner to be well exercised in the Tables of Chap. II. that he may readily know what integers are to be carried from every leffer denomination to the next greater.

49. The following Queftions are defigned to put the learner upon reflection, which will enable him the better to see the nature and use of this Rule.

1. A man was born in the year 1721; when will he be 45 years of age? Anfw. in the year 1766.

2. If after having paid 127. 10's. in part of a debt, there ftill remains due 17. 10s. what was that debt? Anfw. 301. 3. There are two numbers, whofe difference is 17, and the leffer number is 44; what is the greater number? Anfw. 61. 4. A man has 6 bags of Hops; the firft weighs 2 qu. 14lb. and each of the others weighs 14 lb. what quantity has he in all? Anfw. 1C. 1 qu.

5. Received of A three half-pence, of B feven farthings, of C fifteen-pence, of D five groats, of E half a crown, and of F thirty fhillings; how much was received? Anfw. Il. 155. 81 d.

6. Bought a parcel of goods for 401. 10s. paid for packing them 13 s. for carriage 11. 6s. 8d. and expended at making the bargain 15s. 6d. what do the goods ftand me in? Anfw. 431. 55. 2d.

7. Between London and Royston are 33 miles; from thence to Cambridge 10; thence to Newmarket 10; thence to Bury IO; and from thence to Norwich 32 miles: How many miles on this road from London to Norwich? Anfw. 95 miles.

8. How many days are there in the 12 Calendar months, January having 31 days, February 28, March 31, April 30, May 31, June 30, July 31, August 31, September 30, October 31, November 30, and December 31 days? Anfw. 365.

9. How many days are there from the 28th day of March to the 17th day of December in the fame year, both days inclu-` five? Anfw. 265.

10. How many days are there from the 19th day of April, 1748, to the 27th day of November, 1750, both days exclufive? Anfw. 951.

II. A merchant, in the year 1750, imported, by one fhip 8 tuns of Claret, by another 12 tuns 3 hogfheads 42 gallons of Red Port, by another 14 tuns 2 hogfheads 11 gallons of Sherry, and by another 5 tuns 3 hogfheads 10 gallons of Canary; what quantity of wines did he import in all? Anfw. 41 tuns I hogfhead.

12. From the creation of the world to the beginning of the deluge is accounted 1656 years; and from the beginning of the deluge to the birth of Arphaxad, Helvicus reckons 2 years; and thence, to Terah 220 years; thence to the birth of Abraham 70 years (Gen. 11.); thence to the promise given (mentioned Gen. 12.) he reckons 75 years; and thence to the going out of Egypt 430 years; and from that going out, to the Temple of Solomon 480 years; and thence to the birth of Chrift 1015 years; and he fuppofes, that from thence, to the beginning of the common Chriftian or Dionyfian Era 2 years elapfed; and thence, to the present year wherein this was writ, we reckon 1750 years: According to the Chronology of Helvicus, therefore, how long is it fince the creation of the world? Anfw. 5700 years.

13. A furveyor, having meafured 5 feveral pieces of land, finds one of them to contain 7 acres 3 roods 24 perches, another to contain 18 acres 1 rood 16 perches, another_12 acres

C 3

10.